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I Dropped objects hitting the ground at the same time?

  1. Jun 26, 2018 #1
    okay, so I’ve had this random thought. We have all been told that objects fall to the ground at the same speed, even if they have different masses. While it’s true that any two objects, regardless of mass, will accelerate towards Earth at the same speed, that doesn’t mean the Earth is accelerated towards the object at the same speed. Heavier objects have a higher gravitational force, and because of Newton’s Third Law, the Earth expirences the same force towards the object. Because Earth will accelerate towards heavier objects faster, heavier objects dropped in a perfect vacuum will hit the ground before a lighter one.
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  3. Jun 26, 2018 #2


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    It’s more than we have been told, it’s been measured to great accuracy. It’s known as the Galileo experiment. What’s not known if Galileo actually performed it but others have and things fall at the same rate unless air resistance becomes a factor as when feathers are used.


    Often when we try to think our way through these things without fully understanding the math, we get it wrong and that’s what has happened here.

    Here’s a simple discussion on Newton’s law

  4. Jun 27, 2018 #3
    Okay, this is all true, but consider the following scenario.

    You have 2 planets will identical mass and no other forces are acting on the objects is the gravitational force between them. We will name these planets P1 and P2. Because the objects have the same mass as Earth, the objects accelerate to then will be 9.81 m/s^2. So P2 will be falling towards P1 9.81m/s^2. But P1 will be falling towards P2 at the same rate as well. The net rate that the the two planets accelerate towards each other will be 19.62m/s^2 because each object has the same mass and each object is expirencing the same force. Because the objects we experiment with are so small relative to the mass of Earth, the net acceleration towards one another is extremely close to 9.81m/s^2, but the large the mass gets relative to the mass of earth, the higher the net acceleration will be.
  5. Jun 27, 2018 #4
  6. Jun 27, 2018 #5


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    You're right, @Ty Wendland . The adage 'all objects fall at the same rate' is an approximation, valid only when one of the two masses is much larger than the other.
  7. Jun 27, 2018 #6
    Just a random thought I had and wanted feedback on! Thank you!
  8. Jun 27, 2018 #7


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    I'm still concerned that you may think that 2 objects that are both much smaller mass that say the Earth, don't hit the ground at the same time ?
    They do, the experiment has been done and measured countless times
    Astronauts on one of the moon landings even did it on the moon
    The classic hammer and feather experiment

    On earth in an atmosphere, the hammer WILL hit first because of the air resistance the feather encounters, mainly because of its shape

    The experiment was done in a vacuum chamber to negate air resistance and both the hammer and feather hit the ground together

    Prof. Brian Cox did an experiment at a NASA vacuum chamber with a bunch of feathers and a bowling ball


    Last edited: Jun 27, 2018
  9. Jun 27, 2018 #8


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    Me too.
    There is a great temptation to look at these things from the point of view that says "Science got it wrong". I feel that is unhealthy because it neglects the basic authority of what is, in modern times, a very well justified body of work. In all matters Scientific, the actual numbers count and you have to take account of that before thinking that someone has found a loophole. Galilieo's (thought?) experiment shows that 'things fall down with the same acceleration'. That has been demonstrated to be true to greater and greater accuracy over the years.
    What happens between bodies of near equal masses (planets etc.), follows the exact same rules and the same basic equations until General Relativity comes in to it. You just have to look at the real (quantitative) consequences of that.

    The attractive force between two masses m and M is always F = mMG/d2. (G is the universal gravitational constant and not g, d is the distance between the centres of mass of the two objects and both objects are actually heading for their mutual centre of mass )The resulting acceleration of the two bodies will be F/m and F/M. Newton tells us that. Clearly the larger mass will accelerate less than the smaller mass. F/m is the same for any value of m and it only depends on the 'other' mass M.

    So why is it that that Earth seems to be different from the falling ball? Simply because the two accelerations are so different and the Earth's surface accelerates so little, relative to the centre of mass of the two. One easily measurable effect of what happens between two no-dissimilar masses is the wobble of the Earth as the Moon orbits it. The Centre of mass of the two (the Barycentre) is about 4500km from the Earth's centre, which shows that the Earth is pulled into 'an orbit' by the gravity of the Moon. There are no convenient stationary large masses up there to observe how they fall together so we have to imply things from orbiting objects but the centripetal acceleration of the Earth as it orbits round the barycentre is (2Πf)2 r which comes to about 30μm/s2. How much less is the acceleration of the Earth when you drop a 1kg mass - or a 10kg - or a 1000kg? That's why we can say the Earth stays still for the Galileo experiments and why we can use g all over the place.
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  10. Jun 27, 2018 #9


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    Physics being a quantitative science, it's worth calculating the magnitude of this effect and comparing it with all the other experimental uncertainties in any measurement of the time it takes a dropped object to hit the ground. (For example... suppose someone on the other side of the earth happens to fire off an antiaircraft gun while you're running your experiment? And just where is Jupiter right now?)

    As for whether all of this means that it is wrong to say that things "fall at the same speed regardless of their weight"? It's hard to improve on Isaac Asimov's take on this sort of question: https://chem.tufts.edu/answersinscience/relativityofwrong.htm
  11. Jun 27, 2018 #10


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    The same is true for two small object falling on exactly opposite sides of the Earth.
  12. Jun 27, 2018 #11

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    If I remember correctly: Relative to earth, a heavier object would in principle accelerate faster and thus hit the ground after a shorter time compared to a lighter one. This doesn't hold, however, if the the body originates from the earth itself. All terrestrial bodies falling individually fall at exactly the same rate in an ideal scenario.
    Last edited: Jun 27, 2018
  13. Jun 27, 2018 #12


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    As worded the logic of the OP looks fine (with the possible exception of the last sentence), it just doesn't include numbers. I would hope and assume the OP recognizes that a hammer isn't going to accelerate the Earth very much.

    Also, there is a trick to this question depending on the wording in that two objects simultaneously dropped to Earth will impact at the same time, but if dropped separately the fall times will be (very, very slightly) different.
  14. Jun 27, 2018 #13
    I don’t think that objects accelerate to Earth at different speeds, it’s a proven fact that everything accelerated to Earth at 9.81m/s^2. What I’m focused on is the time it two objects, the Earth and some dropped object, to come into contact. Obviously the mass difference between a 1kg object and a 10kg object compared to the Earth is nearly identical, but there is still a difference. In my scenario I’m saying there are no other external forces acting on the two objects besides gravity( which I know is extremely unrealistic). It’s
    more of a hypothetical thought experiment than anything I would apply to the real world.
  15. Jun 27, 2018 #14


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    If you do the maths then two objects of non-negligible masses ##m_1## and ##m_2## will collide in the same time that a small object of negligible mass takes to fall to a large object of mass ##m_1 + m_2##.

    More generally you could search online for the two body gravitational problem and the concept of "reduced mass".
  16. Jun 27, 2018 #15


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    Jupiter? From my calculations, even Pluto has a greater effect on me than I have on the Earth.

    Earth's acceleration towards me: 1.23E-22 m/s2
    My acceleration towards Pluto: 2.59E-14 m/s2 (rough minimum distance)

    Factor: ≈200 million​

    Fun thought experiment.

    Thank you! I've always wondered about this. Never bothered to do the maths till now.
  17. Jun 27, 2018 #16
    I guess that really shows how silly it is to calculate the amount I cause the Earth to accelerate towards me when an object billions of kilometres away has a much greater affect on me than I do the Earth!
  18. Jun 27, 2018 #17
    Given any difference is due to the Earth accelerating towards the object, wouldn't both objects still hit the ground at exactly the same time (if dropped side by side) because the Earth's acceleration would be towards both objects, not just the heavier one?
  19. Jun 27, 2018 #18
    I guess I worded what I was trying to say incorrectly. You are absolutely right. I was thinking more that these “experiments” were done separately, and the times for the objects of different mass were measured separately without influencing one another. I guess this is why I posted this, is so others could find the flaws in my logic!
  20. Jun 27, 2018 #19


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    If we're talking about completely negligible, but in principle present effects, then we also have the direction of the force from each of the objects being different. This means that the Earth will fall a bit sideways, away from the line equidistant from the two objects, and towards the heavier object.
    This in turn - continuing with the unmeasurable physics theme - will mean that due to the surface of the Earth curving away more for the lighter object, it will have a larger distance to cover, and will fall after the heavier one.

    Just to hammer in the obvious - for the m1, m2 << M case, any such difference will be swamped by orders of magnitude-larger errors in measuring instruments, timing of the release, the fact that no floor follows exactly the equipotential surface of the planet. And pretty much anything else one can think of.

    But if one imagines the masses involved as being on a sliding scale, going all the way from m1, m2 << M to m1, m2 >> M, at some point the differences in the rate of falling become important and easy to spot. After all, if we 'drop' the Mars and the Sun on the Earth from 1 AU, they won't hit the ground at the same time.
  21. Jun 27, 2018 #20


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    You may want to start by reading this:


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